The accelerated fully rough turbulent boundary layer

1977 ◽  
Vol 82 (3) ◽  
pp. 507-528 ◽  
Author(s):  
Hugh W. Coleman ◽  
Robert J. Moffat ◽  
William M. Kays
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Stress Tensor ◽  
Skin Friction ◽  
Shape Factor ◽  
Reynolds Shear Stress ◽  
Smooth Wall ◽  
Mean Velocity

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

1974 ◽  
Vol 64 (4) ◽  
pp. 763-774 ◽  
Author(s):  
R. G. Deissler
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Reynolds Shear Stress ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Mass Injection ◽  
The Mean ◽  
Theoretical Results

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analysed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

Mean Velocity, Reynolds Shear Stress, and Fluctuations of Velocity and Pressure Due to Log Laws in a Turbulent Boundary Layer and Origin Offset by Prandtl Transposition Theorem

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Velocity Vector ◽  
Reynolds Shear Stress ◽  
Mean Velocity ◽  
Time Period ◽  
Log Law ◽  
Turbulent Burst

The maxima of Reynolds shear stress and turbulent burst mean period time are crucial points in the intermediate region (termed as mesolayer) for large Reynolds numbers. The three layers (inner, meso, and outer) in a turbulent boundary layer have been analyzed from open equations of turbulent motion, independent of any closure model like eddy viscosity or mixing length, etc. Little above (or below not considered here) the critical point, the matching of mesolayer predicts the log law velocity, peak of Reynolds shear stress domain, and turbulent burst time period. The instantaneous velocity vector after subtraction of mean velocity vector yields the velocity fluctuation vector, also governed by log law. The static pressure fluctuation p′ also predicts log laws in the inner, outer, and mesolayer. The relationship between u′/Ue with u/Ue from structure of turbulent boundary layer is presented in inner, meso, and outer layers. The turbulent bursting time period has been shown to scale with the mesolayer time scale; and Taylor micro time scale; both have been shown to be equivalent in the mesolayer. The shape factor in a turbulent boundary layer shows linear behavior with nondimensional mesolayer length scale. It is shown that the Prandtl transposition (PT) theorem connects the velocity of normal coordinate y with s offset to y + a, then the turbulent velocity profile vector and pressure fluctuation log laws are altered; but skin friction log law, based on outer velocity Ue, remains independent of a the offset of origin. But if skin friction log law is based on bulk average velocity Ub, then skin friction log law depends on a, the offset of origin. These predictions are supported by experimental and direct numerical simulation (DNS) data.

Experimental results for the transpired turbulent boundary layer in an adverse pressure gradient

1975 ◽  
Vol 69 (2) ◽  
pp. 353-375 ◽  
Author(s):  
P. S. Andersen ◽  
W. M. Kays ◽  
R. J. Moffat
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Equation ◽  
Adverse Pressure Gradient ◽  
Stream Velocity ◽  
Pressure Gradients ◽  
Mean Velocity ◽  
Displacement Thickness

An experimental investigation of the fluid mechanics of the transpired turbulent boundary layer in zero and adverse pressure gradients was carried out on the Stanford Heat and Mass Transfer Apparatus. Profiles of (a) the mean velocity, (b) the intensities of the three components of the turbulent velocity fluctuations and (c) the Reynolds stress were obtained by hot-wire anemometry. The wall shear stress was measured by using an integrated form of the boundary-layer equation to ‘extrapolate’ the measured shear-stress profiles to the wall.The two experimental adverse pressure gradients corresponded to free-stream velocity distributions of the type u∞ ∞ xm, where m = −0·15 and −0·20, x being the streamwise co-ordinate. Equilibrium boundary layers (i.e. flows with velocity defect profile similarity) were obtained when the transpiration velocity v0 was varied such that the blowing parameter B = pv0u∞/τ0 and the Clauser pressure-gradient parameter $\beta\equiv\delta_1\tau_0^{-1}\,dp/dx $ were held constant. (τ0 is the shear stress at the wall and δ1 is the displacement thickness.)Tabular and graphical results are presented.

scholarly journals Systematic errors of skin-friction measurements by oil-film interferometry

2015 ◽  
Vol 773 ◽  
pp. 298-326 ◽  
Author(s):  
Antonio Segalini ◽  
Jean-Daniel Rüedi ◽  
Peter A. Monkewitz
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Systematic Errors ◽  
Surface Curvature ◽  
Oil Film ◽  
Oil Films

In recent years, the independent measurement of wall shear stress with oil-film or oil-drop interferometry has become a cornerstone of turbulent-boundary-layer research as many arguments depend critically on a precise knowledge of the skin friction ${\it\tau}_{w}^{\ast }$. To our knowledge, all practitioners of oil-drop interferometry have so far used the leading-order similarity solution for asymptotically thin, wedge-shaped, two-dimensional oil films established by Tanner & Blows (J. Phys. E: Sci. Instrum., vol. 9, 1976, pp. 194–202) to relate the evolution of drop thickness to ${\it\tau}_{w}^{\ast }$. It is generally believed that this procedure, if carefully implemented, yields the true time-averaged ${\it\tau}_{w}^{\ast }$ within $\pm 1\,\%$ or possibly better, but the systematic errors due to the finite thickness of the oil film have never been determined. They are analysed here for oil films with a thickness of the order of a viscous unit in a zero-pressure-gradient turbulent boundary layer. Neglecting spanwise surface curvature and surface tension effects, corrections due to the secondary air boundary layer above the oil film are derived with a linearised triple-layer approach that accounts for the turbulent shear-stress perturbation by means of modified van-Driest-type closure models. In addition, the correction due to processing oil drops with a slight streamwise surface curvature as if they were exact wedges is quantified. Both corrections are evaluated for oil-drop interferograms acquired in a zero-pressure-gradient turbulent boundary layer at a Reynolds number of around 3500, based on displacement thickness, and are shown to produce a reduction of the friction velocity relative to the basic Tanner and Blows theory of between $-0.1\,\%$ and $-1.5\,\%$, depending on the mixing-length model. Despite the uncertainty about the true correction, the analysis allows the formulation of some guidelines on where and when to analyse interference fringes in order to minimise the error on the measured wall shear stress.

The effects of a favourable pressure gradient and of the Reynolds number on an incompressible axisymmetric turbulent boundary layer. Part 1. The turbulent boundary layer

1998 ◽  
Vol 359 ◽  
pp. 329-356 ◽  
Author(s):  
H. H. FERNHOLZ ◽  
D. WARNACK
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Shear Stress ◽  
Wall Shear Stress ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Boundary Layers ◽  
Reynolds Stresses ◽  
The Mean

The effects of a favourable pressure gradient (K[les ]4×10−6) and of the Reynolds number (862[les ]Reδ2[les ]5800) on the mean and fluctuating quantities of four turbulent boundary layers were studied experimentally and are presented in this paper and a companion paper (Part 2). The measurements consist of extensive hot-wire and skin-friction data. The former comprise mean and fluctuating velocities, their correlations and spectra, the latter wall-shear stress measurements obtained by four different techniques which allow testing of calibrations in both laminar-like and turbulent flows for the first time. The measurements provide complete data sets, obtained in an axisymmetric test section, which can serve as test cases as specified by the 1981 Stanford conference.Two different types of accelerated boundary layers were investigated and are described: in this paper (Part 1) the fully turbulent, accelerated boundary layer (sometimes denoted laminarescent) with approximately local equilibrium between the production and dissipation of the turbulent energy and with relaxation to a zero pressure gradient flow (cases 1 and 3); and in Part 2 the strongly accelerated boundary layer with ‘inactive’ turbulence, laminar-like mean flow behaviour (relaminarized), and reversion to the turbulent state (cases 2 and 4). In all four cases the standard logarithmic law fails but there is no single parametric criterion which denotes the beginning or the end of this breakdown. However, it can be demonstrated that the departure of the mean-velocity profile is accompanied by characteristic changes of turbulent quantities, such as the maxima of the Reynolds stresses or the fluctuating value of the skin friction.The boundary layers described here are maintained in the laminarescent state just up to the beginning of relaminarization and then relaxed to the turbulent state in a zero pressure gradient. The relaxation of the turbulence structure occurs much faster than in an adverse pressure gradient. In the accelerating boundary layer absolute values of the Reynolds stresses remain more or less constant in the outer region of the boundary layer in accordance with the results of Blackwelder & Kovasznay (1972), and rise both in the vincinity of the wall in conjunction with the rising wall shear stress and in the centre region of the boundary layer with the increase of production.

Calculation of a Turbulent Boundary Layer Downstream of a Small Step Change in Surface Roughness

1975 ◽  
Vol 26 (3) ◽  
pp. 202-210 ◽  
Author(s):  
R A Antonia ◽  
D H Wood
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Reynolds Shear Stress ◽  
Step Change ◽  
Rough Wall ◽  
Small Step ◽  
Mean Velocity ◽  
Good Agreement

SummaryMeasurements of mean velocity and Reynolds shear stress have been made in a turbulent boundary layer downstream of a small step change in surface roughness. Upstream of the step the surface is smooth, while downstream it consists of a d-type rough wall made up by a series of two-dimensional elements of square cross section placed transversely across the flow and spaced one element width apart in the direction of the flow. The calculated mean velocity and Reynolds shear stress profiles obtained using the method of Bradshaw, Ferriss and Atwell are in good agreement with the measurements throughout the relaxation region of the layer. Well downstream the calculation method adequately reproduces the self-preserving features of a d-type rough wall.

A New Integral Method for Analyzing the Turbulent Boundary Layer With Arbitrary Pressure Gradient

1969 ◽  
Vol 91 (3) ◽  
pp. 371-376 ◽  
Author(s):  
F. M. White
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Pressure Gradient ◽  
Skin Friction ◽  
Shape Factor ◽  
Single Equation ◽  
Skin Friction Coefficient ◽  
New Method ◽  
Momentum Thickness ◽  
New Approach

For routine calculations of the properties of the incompressible turbulent boundary layer with arbitrary pressure gradient, the presently accepted method is the Karman integral technique, which consists of three simultaneous equations, the three unknowns being the momentum thickness, the skin friction, and the shape factor. Considerable empiricism is contained in the Karman method, so that the reliability is only fair. The present paper derives an entirely new method, based upon a suggestion of R. Brand and L. Persen. The new approach results in a single equation for the skin friction coefficient, with the only parameter being the nominal Reynolds number and the only empiricism being a single assumption about the effect of pressure gradient. No other variables, such as shape factor or momentum thickness, are needed, although they can of course be calculated as byproducts of the analysis. The new method also contains a built-in separation criterion, which was the most glaring omission of the Karman technique. Agreement with experiment is as good or better than the most reliable Karman methods in use today.

On turbulent boundary-layer separation

1968 ◽  
Vol 32 (2) ◽  
pp. 293-304 ◽  
Author(s):  
V. A. Sandborn ◽  
C. Y. Liu
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Analytical Study ◽  
Boundary Layer Separation ◽  
Mean Velocity ◽  
Laminar Separation ◽  
Layer Separation ◽  
Turbulent Separation ◽  
Separation Model

An experimental and analytical study of the separation of a turbulent boundary layer is reported. The turbulent boundary-layer separation model proposed by Sandborn & Kline (1961) is demonstrated to predict the experimental results. Two distinct turbulent separation regions, an intermittent and a steady separation, with correspondingly different velocity distributions are confirmed. The true zero wall shear stress turbulent separation point is determined by electronic means. The associated mean velocity profile is shown to belong to the same family of profiles as found for laminar separation. The velocity distribution at the point of reattachment of a turbulent boundary layer behind a step is also shown to belong to the laminar separation family.Prediction of the location of steady turbulent boundary-layer separation is made using the technique employed by Stratford (1959) for intermittent separation.

Turbulent Boundary Layer Subjected to a Sudden Change in Surface Roughness and Temperature

1999 ◽  
Author(s):  
João Henrique D. Guimarães ◽  
Sergio J. F. dos Santos ◽  
Jian Su ◽  
Atila P. Silva Freire
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Turbulent Boundary Layer ◽  
Skin Friction ◽  
Sudden Change ◽  
Stanton Number ◽  
Temperature Profiles ◽  
Internal Layers ◽  
Mean Velocity ◽  
Wall Boundary Conditions

Abstract In present work, the dynamic and thermal behaviour of flows that develop over surfaces that simultaneously present a sudden change in surface roughness and temperature are discussed. In particular, the work is concerned with the physical validation of a newly proposed formulation for the near wall temperature profile. The theory uses the concept of the displacement in origin, together with some asymptotic arguments, to propose a new expression for the logarithmic region of the turbulent boundary layer. The new expressions are, therefore, of universal applicability, being independent of the type of rough surface considered. The present formulation may be used to give wall boundary conditions for two-equation differential models. The theoretical results are validated with experimental data obtained for flows that develop over flat surfaces with sudden changes in surface roughness and in temperature conditions. Measurements of mean velocity and of mean temperature are presented. A reduction of the data provides an estimate of the skin-friction coefficient, the Stanton number, the displacement in origin for both the velocity and the temperature profiles, and the thickness of the internal layers for the velocity and temperature profiles. The skin-friction co-efficient was calculated based on the chart method of Perry and Joubert (J.F.M., 17, 193–211, 1963) and on a balance of the integral momentum equation. The same chart method was used for the evaluation of the Stanton number and the displacement in origin.

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